Middle School Students’ Reasoning in Nonlinear Proportional Problems in Geometry

In this study, we investigate sixth, seventh, and eighth grade students’ achievement in nonlinear (quadratic or cubic) proportional problems regarding length, area, and volume of enlarged figures. In addition, we examine students’ solution strategies for the problems and obstacles that prevent students from answering the problems correctly by using a mixed method research design. A total of 935 middle school students were given a paper-pencil test and 12 of them were interviewed. Findings indicated that achievement of the participants were low and that students used a limited number of strategies for solving the problems. In addition, these strategies were found to have lacked the argument of the linear proportional and nonlinear proportional relationships among length, area, and volume concepts for most of the participants’ answers. Moreover, analysis revealed that the confusion of linear proportional and nonlinear proportional relationships and misinterpretation of additive and multiplicative relationships were serious obstacles while solving the nonlinear proportional problems related to the area and volume of enlarged figures.     

Nature watch

The Sunderbans is the largest mangrove vegetation in the world. Changes in the environment, particularly driven by climate change, forewarn us of the dwindling diversity of exclusive mangrove plants and the charismatic animal species–especially the tiger. The Sunderbans, with its fast-changing geomorphic and hydrological character, is creeping towards its doomsday.